The streptococci bacteria population N at time t (in months) is given by N = N0e 2t where N0 is the initial population. If the initial population was 100, how long does it take for the population to reach one million?

Answer:

[tex]A = 74.7^\circ[/tex]

[tex]B = 42.5^\circ[/tex]

[tex]C = 62.8^\circ[/tex]

Step-by-step explanation:

Given

[tex]A = (-1,2) \to (x_1,y_1)[/tex]

[tex]B = (2,8) \to (x_2,y_2)[/tex]

[tex]C = (4,1) \to (x_3,y_3)[/tex]

Required

The measure of each angle

First, we calculate the length of the three sides of the triangle.

This is calculated using distance formula

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2[/tex]

For AB

[tex]A = (-1,2) \to (x_1,y_1)[/tex]

[tex]B = (2,8) \to (x_2,y_2)[/tex]

[tex]d = \sqrt{(-1 - 2)^2 + (2 - 8)^2[/tex]

[tex]d = \sqrt{(-3)^2 + (-6)^2[/tex]

[tex]d = \sqrt{45[/tex]

So:

[tex]AB = \sqrt{45[/tex]

For BC

[tex]B = (2,8) \to (x_2,y_2)[/tex]

[tex]C = (4,1) \to (x_3,y_3)[/tex]

[tex]BC = \sqrt{(2 - 4)^2 + (8 - 1)^2[/tex]

[tex]BC = \sqrt{(-2)^2 + (7)^2[/tex]

[tex]BC = \sqrt{53[/tex]

For AC

[tex]A = (-1,2) \to (x_1,y_1)[/tex]

[tex]C = (4,1) \to (x_3,y_3)[/tex]

[tex]AC = \sqrt{(-1 - 4)^2 + (2 - 1)^2[/tex]

[tex]AC = \sqrt{(-5)^2 + (1)^2[/tex]

[tex]AC = \sqrt{26[/tex]

So, we have:

[tex]AB = \sqrt{45[/tex]

[tex]BC = \sqrt{53[/tex]

[tex]AC = \sqrt{26[/tex]

By representation

[tex]AB \to c[/tex]

[tex]BC \to a[/tex]

[tex]AC \to b[/tex]

So, we have:

[tex]a = \sqrt{53[/tex]

[tex]b = \sqrt{26[/tex]

[tex]c = \sqrt{45[/tex]

By cosine laws, the angles are calculated using:

[tex]a^2 = b^2 + c^2 -2bc \cos A[/tex]

[tex]b^2 = a^2 + c^2 -2ac \cos B[/tex]

[tex]c^2 = a^2 + b^2 -2ab\ cos C[/tex]

[tex]a^2 = b^2 + c^2 -2bc \cos A[/tex]

[tex](\sqrt{53})^2 = (\sqrt{26})^2 +(\sqrt{45})^2 - 2 * (\sqrt{26}) +(\sqrt{45}) * \cos A[/tex]

[tex]53 = 26 +45 - 2 * 34.21 * \cos A[/tex]

[tex]53 = 26 +45 - 68.42 * \cos A[/tex]

Collect like terms

[tex]53 - 26 -45 = - 68.42 * \cos A[/tex]

[tex]-18 = - 68.42 * \cos A[/tex]

Solve for [tex]\cos A[/tex]

[tex]\cos A =\frac{-18}{-68.42}[/tex]

[tex]\cos A =0.2631[/tex]

Take arc cos of both sides

[tex]A =\cos^{-1}(0.2631)[/tex]

[tex]A = 74.7^\circ[/tex]

[tex]b^2 = a^2 + c^2 -2ac \cos B[/tex]

[tex](\sqrt{26})^2 = (\sqrt{53})^2 +(\sqrt{45})^2 - 2 * (\sqrt{53}) +(\sqrt{45}) * \cos B[/tex]

[tex]26 = 53 +45 -97.67 * \cos B[/tex]

Collect like terms

[tex]26 - 53 -45= -97.67 * \cos B[/tex]

[tex]-72= -97.67 * \cos B[/tex]

Solve for [tex]\cos B[/tex]

[tex]\cos B = \frac{-72}{-97.67}[/tex]

[tex]\cos B = 0.7372[/tex]

Take arc cos of both sides

[tex]B = \cos^{-1}(0.7372)[/tex]

[tex]B = 42.5^\circ[/tex]

For the third angle, we use:

[tex]A + B + C = 180[/tex] --- angles in a triangle

Make C the subject

[tex]C = 180 - A -B[/tex]

[tex]C = 180 - 74.7 -42.5[/tex]

[tex]C = 62.8^\circ[/tex]

Answer:

F

you have to set it up as an equation then solve

Set end gulf g if NC gba has 4th s 3 eggs $"4 runs they've eggs her Seth w if rid the ms has hehe he na na

Answer:

No, no, yes, yes

Step-by-step explanation:

3.072 is not bigger than 3.2, so incorrect (no)

728.307 is not bigger than 729.078, so incorrect again (no)

12.040 does equal 12.04, so correct (yes)

531.135 is smaller than 531.315, so correct (yes)

Answer:

9y^4

Step-by-step explanation

i believe you just add 6yand 3y

hope this helps :)

if this is a test wait for someone else to confirm just to make sure

Answer:

Vertical Angles

Step-by-step explanation:

Hope this helps

Answer:

WHAT!? THEY BOTH GOT BANNED?! HOW

Answer:

h(4)=-21

Step-by-step explanation:

h(v)=5x^2-28v+11

h(4)=5(4)^2-28(4)+11

h(4)=5(16)-112+11

h(4)=80-101

h(4)=-21

If this helps please mark as brainliest

Answer:

1.9

Step-by-step explanation:

just put it into he calculator, because with 3 above the square root.

Answer:

Approximately 1.9 (rounded to the nearest tenth)

Step-by-step explanation:

First, we are left off with the equation:

[tex]y^{3} = 7[/tex]

We know we want to solve for y. So, let's do the opposite of what is being done to y. In other words, let's find the cube root of [tex]y^{3} = 7[/tex].

[tex]\sqrt[3]{y^3} = \sqrt[3]{7}[/tex]

Then, the [tex]\sqrt[3]{y^3}[/tex] just simplifies to y. On the other side, we cannot find the cube root of 7 in our minds, so that is why it tell us to use a calculator. So...

y = 1.9

Therefore, the cube root of 7 is around 1.9. Hope this helps!

Answer:

1 (2/3)meter

Step-by-step explanation:

3(1/2) = 7/2  = 21/6

1(5/6) = 11/6

21/6 - 11/6 =  10/6 = 5/3 = 1 (2/3)

Answer:

dividend,  

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

It can't be B or D, because there is only a difference in the X axis (Meaning it goes either left or right)

It can't be A because 2 is less than 11, so (2, -1) would be left 9 units in relation to (11, -1)

Answer:

answer for yes total, is 5, the answer for no total is 20, the total for junior is 17, and the total for senior is 8.

Step-by-step explanation:

What you do is you add the 2 values. for example, to find the total for the juniors, you would add 1 to 16.

Answer:

The true statements are

3/5 is the base

3 is the exponent

(3/5)³ = 3/5 × 3/5 × 3/5

(3/5)³ = 27/125

Step-by-step explanation:

Let a and b be any integer, given the expression;

[tex]a^b[/tex]

a is the base

b is the exponent

Similarly if we have;

[tex]a^3[/tex]

This means we can multiply a in three places as shown;

[tex]a^3 = a \times a \times a[/tex]

Applying this to the given expression

[tex](\frac{3}{5} )^3 = \frac{3}{5} \times \frac{3}{5} \times \frac{3}{5} \\Also\\(\frac{3}{5} )^3 = \frac{3 \times 3 \times 3}{5 \times 5 \times 5} \\(\frac{3}{5} )^3 = \frac{27}{125}[/tex]

The base value will be 3/5 and the exponent is 3

Answer:

21, 18, 15

Step-by-step explanation:

First term = a1

Second term = a2

Third term = a3

a1 = 21

a2

= a + d

= 21 - 3

= 18

a3

= a + 2d

= 21 + 2 ( - 3 )

= 21 - 6

= 15

The first 3 terms are 21, 18, 15.

Answer:

The probability of choosing 3 kings and 4 queens out of the 8 (4+4) kings and queens is given by 0.42857

Step-by-step explanation:

There are 4 queens and 4 kings in a deck of 52 cards. So we have to choose 5 cards having 3 queens and 2 kings out of the 52

Therefore the combinations can be written like this 8C5= 56 ways

And the probability this can be chosen is  given by

4C3*4C2/8C5

=4*6/56

=24/56

=0.42857

The probability of choosing 2 kings and 3 queens out of the 8 (4+4) kings and queens is given by 0.42857 or 24/56

Answer:

Step-by-step explanation:

3) JH is the length of the radius

def. of midpoint

def. of < bisector

4) The missing length is 15

Given a=8 and c=17,

b = 30

∠α = 28.072° = 28°4'21" = 0.48996 rad

∠β = 61.928° = 61°55'39" = 1.08084 rad

area = 60

perimeter = 40

h =  

120

17

= 7.0588235294118

Step-by-step explanation:

The answer is scalene triangle

Answer:

21

Step-by-step explanation:63

Answer:

- 3

Step-by-step explanation:

ap ex

Answer:

Parallelogram

Step-by-step explanation:

Answer:

The correct  expression to calculate the number of bees after t  days if the initial swarm had 1000 bees is [tex]P = 1000 *e^{0.2*t}[/tex]

Step-by-step explanation:

Given -

The population of a swarm of killer bees increases by 10 times in 50 days

The rate of increase of population is [tex]r = \frac{10}{50} = 0.2[/tex] per day

As we now the equation of population projection is

[tex]P= P_0 *e^{rt}\\[/tex]

Where P0 = initial population

P is the population after time t

and r is the rate of increase of population

Substituting the given values in above equation, we get -

[tex]P = 1000 *e^{0.2*t}[/tex]

Answer:

1/6

Step-by-step explanation:

y2 - y1 / x2 - x1

6 - 5 / 4 - (-2)

1 / 6

1/6

Answer:

14 square cm Should be the answer, plz do correct me if im wrong!!

Step-by-step explanation:

The right side which is triangle is 2x3 is 6 but because there is only half 6/2

it is 3!

Th middle portion which is square is 2 to the 4th power or 2x2x2x2 or just 2x4(2^4)!! Which is 8!

Finally the last triangle is the same as the first 3

8+6(the to triangles 3+3)=14

Mark brainliest plz, it was nice helping you if im wrong plz tell me immdiately i dont want to cause any problems good day ;)

Answer:

55 degrees is the measure of the unknown angle

Answer:

give brainliest

Step-by-step explanation:

then i help

Answer:

False, The dilation could decrease as well as increase the length of figure or line segment depending on the scale factors it's being dilated by.

Hope this helps!